Advanced Corporate Finance. 3. Capital structure

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Eileen Chapman
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1 Advanced Corporate Finance 3. Capital structure

2 Objectives of the session So far, NPV concept and possibility to move from accounting data to cash flows => But necessity to go further regarding the discount rate to use. This session s objectives: 1. Understand the impact of the capital structure on the value of the firm in a world with and without taxes 2. Understand the impact of the capital structure on the cost of capital in a world with and without taxes 3. Set the theoretical model in perspective with real world observations 2

3 Practice of corporate finance: evidence from the field Graham & Harvey (2001) : survey of 392 CFOs about cost of capital, capital budgeting, capital structure. «..executives use the mainline techniques that business schools have taught for years, NPV and CAPM to value projects and to estimate the cost of equity. Interestingly, financial executives are much less likely to follow the academically prescribed factors and theories when determining capital structure» Are theories valid? Are CFOs ignorant? Are business schools better at teaching capital budgeting and the cost of capital than at teaching capital structure? 3

4 Cost of Capital with Debt Up to now, the analysis has proceeded based on the assumption that investment decisions are independent of financing decisions. Does the value of a company change the cost of capital change if leverage changes? If so, how to compute the impact of the financing decision on the company value? 4

5 Example CAPM holds Risk-free rate = 5%, Market risk premium = 6% Consider an all-equity firm: Market value V 100 Beta Equity 1 Cost of capital 11% (=5% + 6% * 1) Now consider borrowing 20 to buy back shares. Why such a move? Debt is cheaper than equity Replacing equity with debt should reduce the average cost of financing What will be the final impact On the value of the company? (Equity + Debt)? On the weighted average cost of capital (WACC)? 5

6 The intuition (no tax) In perfect market (no tax) 20% debt 80% equity = 40% debt 60% equity 6

7 Balance sheet in market values The principle of the sum of the parts V U = E + D In perfect market (no tax) r A = WACC; β A = β wacc Value of all-equity firm: Value of equity: E r E ; β E V U Value of debt: r D ; β D D E r = WACC = r + r V A E D D V 7

8 Weighted Average Cost of Capital (WACC) An average of: In perfect market (no tax) The cost of equity r equity The cost of debt r debt Weighted by their relative market values (E/V and D/V) r wacc r equity E V + r debt D V Note: V = E + D 8

9 Modigliani Miller (1958) Assume perfect capital markets: no taxes, no transaction costs, no asymmetry of information. Proposition I: Proposition II: The market value of any firm is independent of its capital structure: V = E+D = Assets = V U The weighted average cost of capital is independent of its capital structure r wacc = r A In perfect market (no tax) r A is the cost of capital of an all-equity firm (unlevered) NB: Whatever the capital structure, the total assets of the firm remain constant here 9

10 In Practice Value of company: V = 100 In perfect market (no tax) Initial Final Equity Debt 0 20 Total 100 = 100 (MM I) WACC = r A 11% = 11% (MM II) Cost of debt - 5% (assuming risk-free debt) D/V Cost of equity 11% 12.50% (to obtain WACC = r A = 11%) E/V 100% 80% 10

11 Why do we observe a constant r wacc? Consider someone owning a portfolio of all firm s securities (debt and equity) with X equity = E/V (80% in example ) and X debt = D/V (20%) Expected return on portfolio = r equity * X equity + r debt * X debt This is equal to the WACC (see definition): r portoflio = r wacc But she/he would, in fact, own the company. The expected return would be equal to the expected return of the unlevered (all-equity) firm r portoflio = r A The weighted average cost of capital is thus equal to the cost of capital of an all-equity firm r wacc = r A In perfect market (no tax) 11

12 How are MM I and MM II related? Assume (to simplify the presentation): Perpetuities EBIT = FCF In perfect market (no tax) For a levered company, earnings before interest and taxes will be split between interests payment and dividends payment EBIT = Int + Div Market value of equity: present value of future dividends discounted at the cost of equity E = Div / r E Market value of debt: present value of future interests discounted at the cost of debt D = Int / r D 12

13 Relationship between the value of company and WACC From the definition of the WACC: r wacc * V = r equity * E + r debt * D As r equity * E = Div and r debt * D = Int r wacc * V = EBIT In perfect market (no tax) V = EBIT / r wacc Market value of levered firm EBIT is independent of leverage If value of company does not vary with leverage (MM I), neither does the WACC (MM II) 13

14 MM II and the cost of equity (no tax) The equality WACC = r A can also be written: r = r + ( r r ) E A A D The expected return on equity is a growing function of the leverage ratio r 12.5% 11% r A D E r E Additional cost of equity due to leverage WACC In perfect market (no tax) Observable Implicit 5% 0.25 r D D/E 14

15 Why does r equity increases with leverage? Because leverage increases the risk of equity. To see this, back to the portfolio with both debt and equity. In perfect market (no tax) Beta of portfolio: portfolio = equity * X equity + debt * X debt But also: portfolio = Asset Consider A as a given by nature which does only depend on company activity (independently from the leverage ratio) So: Asset E = Equity + E + D Debt E D + D or Equity = + ( ) Asset Asset Debt D E 15

16 Back to our example Consider a risk-free debt In perfect market (no tax) E = A(1 + D ) = A E V E 20 E = 1 (1 + ) = r = r + ( r r ) = 5% + 6% 1.25 = 12.50% E F M F E 16

17 Capital structure in perfect markets Wrap-up To finance operations, firms issue debt or equity In perfect market (no tax) Capital Structure : firm s mix of securities Does this mix selection affect firm value? Miller & Modigliani (MM) say NO (in perfect capital markets) Firm value is determined by its real assets value is independent of capital structure Capital structure is irrelevant (for fixed investment decisions, no taxes, no costs of financial distress) Allows separation of investment and financing decisions 17

18 However we are not in a perfect world Let us add one complexity: suppose we are in perfect capital markets, except one imperfection: corporates have to pay taxes Interests are tax deductible => tax shield Tax savings Transfer of value from the State to the company Tax shield = Interest payment Corporate Tax Rate = (r D D) T C r D : cost of new debt D : market value of debt How valuable is the corporate tax shield? Compute the PV of the tax shield Assuming permanent borrowing: Value of levered firm = Value if all-equity financed + PV(Tax Shield) V L = V U + T C D In perfect market with tax (and perpetual debt) PV( TaxShield) = T r r D D C D = T C D 18

19 The intuition (with taxes) 20% debt 80% equity < 40% debt 60% equity 19

20 Balance sheet in market values Back to the principle of the sum of the parts V U + T c D = E + D In perfect market with tax (and perpetual debt) r A ; β A Value of all-equity firm: Value of equity: E r E ; β E V U r D ; β D Value of tax shield: PV(TS) Value of debt: D r D ; β D r A V V U L + r D Tc D V L = r E E V L + r D D V L 20

21 A Numerical Illustration B In perfect market with tax (and perpetual debt) Balance Sheet Total Assets 1,000 1,000 Book Equity 1, Debt (8%) Income Statement EBIT Interest 0 40 Taxable Income Taxes (40%) Net Income Dividend Interest 0 40 Total Assume r A = 10% (1) Value of all-equity-firm: V U = 144 / 0.10 = 1,440 (2) PV(Tax Shield): Tax Shield = 40 x 0.40 = 16 PV(Tax Shield) = 16/0.08 = 200 (3) Value of levered company: V L = 1, = 1,640 (4) Market value of equity: E L = V L - D = 1, = 1,140 21

22 WACC and leverage Assume (to simplify the presentation): Perpetuities NOPAT = net operating profit after taxes = FCF In perfect market with tax (and perpetual debt) NOPAT = Net Income + Interest - Tax Shield = (EBIT r D D) (1 T C ) + r D D - T C r D D = Net Income for all-equity firm = EBIT (1 T C ) V L = NOPAT / WACC r E + r (1 T ) D = EBIT (1 T ) = NOPAT E D C C E D WACC = r E rd (1 TC ) V + V L L In our example (perpetual debt): NOPAT = 144 WACC = 10.53% x % x 0.60 x 0.31 = 8.78% V L = NOPAT / WACC = 144 / 8,78% = 1,640 22

23 What does WACC do? In perfect market with tax The WACC includes all impacts from the financial structure (which all goes into the denominator of the present value calculation) The WACC decreases with leverage, only because of the tax shields WACC is the discount rate used to calculate directly the market value of the levered firm by discounting the NOPAT (which is, by definition, independent from the financial structure) V = EBIT*(1-T c )/ WACC Market value of levered firm EBIT is independent of leverage If value of company varies with leverage, so does WACC in opposite direction 23

24 The WACC in perfect market with tax: an interpretation General definition (in perfect market, with corporate tax): In perfect market with tax E D WACC = re + rd (1 TC ) V V L L All financing items: the average financing cost of the levered company With perpetual debt: V U WACC = ra ra VL In perfect market with tax (and perpetual debt) Cost of assets = the expected return of the same company if entirely equity financed In our example: V L = 1,640 WACC = 10.53% x % x 0.60 x 0.31 = 8.78% < r A = 10% 24

25 Unlevered Vs Levered Values In perfect market with tax r A is the cost of capital (or equity) of an all-equity firm, i.e. the cost of assets It is the discount rate that allows to compute the unlevered (i.e. all-equity ) company value in one single calculation: V U = EBIT(1-T C )/r A r A does not embed any effect from the financial structure (it is independent from the financial structure) The Weighted Average Cost of Capital (WACC) is the discount rate that allows to compute the total levered company value in one single calculation: V L = EBIT(1-T C )/WACC As such, the WACC embeds the effects from the financial structure if any (those are not embedded in the numerator of the PV formula, as NOPAT (= EBIT(1-T C )) is independent from the financial structure) 25

26 What about the cost of equity? In perfect market with tax (and perpetual debt) 1) Cost of equity increases with leverage: r E = r + ( r r ) (1 T ) A D 2) Beta of equity increases A = + ( )(1 T ) E A A D C C D E D E Proof: E = ( EBIT rd D) (1 T r But V U = EBIT(1-T C )/r A and E = V U + T C D D Replace and solve E C ) In our example (perpetual debt): r E = 10% +(10%-8%)(1-0.4)(500/1,140) = 10.53% or r E = Div/E = 120/1,140 = 10.53% 26

27 MM and the cost of equity In perfect market with tax (and perpetual debt) The expected return on equity is still a growing function of the leverage ratio re = ra + ( ra rd ) D (1 TC ) E The WACC is now a decreasing function of the leverage (due to tax shields only) r r A r E Additional cost of equity due to leverage r A WACC Observable Implicit 0.25 r D D/E 27

28 Conclusion on our initial issue Question: What happens when the firm increases leverage? MM (perfect capital markets) MM (with taxes) To the company value? (V L ) Unchanged Increases To the equity value? (E) Unchanged Increases To the cost of capital? (WACC) Unchanged Decreases To the cost of equity? (r E ) Increases Increases (less) 28

29 What if debt is not permanent? > EBITDA Dep EBIT Interest Taxes (Tc = 40%) Earnings CFop CFinv DIV Debt Book eq ,000 1,000 Debt

30 Company Valuation 1. Value of unlevered company (with perpetual FCF u ) Free Cash Flow unlevered = 144 V U = FCF U / r A = 144 / 0.10 = 1, PV(Taxshield) PV TaxShield) = (1.08) (1.08) (1.08) (1.08) ( = Value of levered company V = 1, = Value of equity E = =

31 What about Personal Taxes? Suppose operating income = 1 If paid out as Interest Equity income Corporate tax 0 T C Income after corporate tax T C Personal tax T P T PE (1-T C ) Income after all taxes 1- T P (1-T PE )(1-T C ) 31 With T C corporate Tax, T P personal tax on interest income, T PE, personal tax on equity income. NB: Marginal Rates!

32 PV(TaxShield) with corporate and personal taxes At the investor level, tax advantage of debt is positive if: 1-T P >(1-T C )(1-T PE ) PV( TaxShield) (1 TC )(1 TPE) = [1 ] D (1 T ) P Note: if T P = T PE, then PV(TaxShield) = T C D NB: Tax advantages may heavily change from one country to the other because taxation differs! But also whitin country => function of the situation of each investor 32

33 Where does the PV(TaxShield) formula come from? After taxes income for Total Stockholders Debt holders ( EBIT rd D)(1 TC )(1 TPE) r D D( 1 TP ) ( EBIT rd D)(1 TC )(1 TPE) + rd D(1 TP ) This can be written as: EBIT(1 T C )(1 T PE ) + r D D(1 T P (1 TC )(1 T ) (1 (1 T ) P PE ) Market values V u D Tax level 33

34 What about the real world? Huge differences regarding leverage Industry influence Cash balances (and thus reflection to have in terms of net debt) Low amount of debt for some industries puzzle? If PV(Tax Shield) > 0, why not 100% debt? Or a high figure well above 50% for example? Several explanations have been suggested Limits to tax benefits of debt => need to have taxable earnings (not really the case for start-ups or new high tech companies). Optimally, in theory, from tax savings perspective EBIT = interest payments => 0 tax! But there are limits to this! 34

35 What about the real world? Empirical Evidence => Internationally low level of leverage (20%-40%) firms do not seem to exploit the full benefits of leverage Graham (2000) estimates that tax benefits of interest deductibility represent 9.7% of market value for a typical firm Two counterbalancing forces: cost of financial distress As debt increases, probability of financial problem increases agency costs Conflicts of interest between shareholders and debtholders Interest payments MUST be made... There is obviously more flexibility regarding dividends => firms with unstable earning may be more reluctant to use leverage at a high level 35

36 Market value What if we add bankruptcy and agency costs? Trade-off theory PV(costs of financial distress and agency costs) PV(Tax Shield) Value of all-equity firm 36 Optimal Debt ratio = ratio of debt which maximizes the company value Debt ratio 36

37 What about the real world? Increasing debt increasing risk and increasing likelihood of distress, which has costs associated with it, such as: Costs of potential bankruptcy Costs associated with potential conflict shareholders-bondholders 1. Costs associated with the inability to operate efficiently, examples: a. Incentive to take large risks b. Incentive toward underinvestment 2. Other costs, example: a. Milking the property b. Costs of bond provisions / compliance 37

38 Example assumptions: D=150 Discount rate = 0% Agency costs 1. Incentive to take large risks (1/3) Low-risk project (market value) V = E + D Recession (p=0,5) 100 = Boom (p=0,5) 200 = Value 150 =

39 Example assumptions: D=150 Discount rate = 0% Agency costs 1. Incentive to take large risks (2/3) High-risk project (market value) V = E + D Recession (p=0,5) 20 = Boom (p=0,5) 270 = Value 145 =

40 Agency costs 1. Incentive to take large risks (3/3) Low-risk project: V=150 E=25 D=125 High-risk project: V=145 E=60 D=85 The low-risk project has a higher value than the high-risk project Shareholders choice? Shareholders expropriate value from the bondholders Other similar issues: - Underinvestment - Milking properties 40

41 Example assumptions: D=400 Discount rate = 0% Agency costs 2. Incentive toward underinvestment (1/3) Initial situation (market value) V = E + D Recession (p=0,5) 240 = Boom (p=0,5) 500 = Value 370 =

42 Example assumptions: D=400 Discount rate = 0% Agency costs 2. Incentive toward underinvestment (2/3) Firm with new project: New shares issued 100 Euro V = E + D Recession (p=0,5) 410 = Boom (p=0,5) 670 = Value 540 =

43 Agency costs 2. Incentive toward underinvestment (3/3) No project: V = 370 E = 50 D = 320 Project: V = 540 E = 140 D = 400 NPV = 170 E increases by 90 but shareholders invested 100 Positive NPV project could not be undertaken because of conflicts of interests 43

44 Agency costs 3. Milking the property When D is very risky, shareholders may: pay out extra dividends (no investments) new debt to pay extra dividends Protective covenants when debt is issued 44

45 Ways to mitigate agency costs Negative covenants prohibiting actions that the company may take Limitation of payout Firm may not pledge any of its assets to other lender No sell or lease its major assets without approval No issue of additional debt Positive covenants specifies an action that a company agrees Maintain working capital at a minimum level Periodical reporting 45

Advanced Corporate Finance. 3. Capital structure

Advanced Corporate Finance. 3. Capital structure Advanced Corporate Finance 3. Capital structure Practical Information Change of groups! A => : Group 3 Friday 10-12 am F => N : Group 2 Monday 4-6 pm O => Z : Group 1 Friday 4-6 pm 2 Objectives of the